Let $G=\langle a,b\rangle$ be a finite $p$-group such that $a^p=b^p=1$. Is there any result about the size of the set of $p$-elements $\Omega(G):=\{g\in G\mid g^p=1\}$? In particular, I'm interested in the fraction $|\Omega(G)|/|G|$.
Edit: I was exactly wondering about if the fraction $|Ω(G)|/|G|$ could be done arbitrarily small in this class of groups. I'm not able to find a reference to this (or conversely a theorem that states the existence of a positive lower bound $c$).